If you horizontally compress the exponential function f(x) = 2* by a factor of
5, which of these is the equation of the new function?
A. f(x) = 10x
B. f(x) = 5(2)
C. f(x) = 2(5x)
D. f(x) = 7*
UBMIT
Answers
The new function's mathematical formula f(x) is 7*.
How does an exponential work?A mathematical function termed an exponential function has the formula f (x) = ax, where x is a variable and a constant called the base of the function, which must be greater than 0. The transcendental number, or e, which is roughly equivalent to 2.71828, is the most often used exponential function basis.Your function must be exponential if it can be expressed as y = a b x, where and are constants, a 0 and b > 0 and b 1 respectively. You always have functions to the second power in quadratic equations. A variable is used as the exponent in exponential functions.To learn more about exponential function refer to:
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Answer: the answer is f(x)=2^(5x)
Step-by-step explanation:
step 1: do the math and divide numbers by more numbers.
Step 2: then add the exponent to another exponent which is a variable.
step 3: then combine the common denominators and you have your answer!
Related Questions
What does 1 2 scale mean?
Answers
If the scale factor is a fraction, the shape will be smaller. This is called reduction. Therefore, a 1/2 scaling factor means that the new shape is half of the original shape.
What is 1 2 scale?Half scale is 1:2. It is helpful to think of this as one unit on the drawing equals two units on the object. A small object can be enlarged on the paper and drawn in 2:1 scale. This means the drawing of the object is twice as large as the object itself.This means that one unit on the page represents one unit in 'real life'. If a drawing is drawn HALF the actual size of the object, the scale is 1:2. This means that one unit on the page is equal to two units in real life.They are a reference to the original drawing size. For example, if a drawing file is currently sized at 24″x36″, then a full size print of that file would be 24″x36″. A half size print, or 50% reduction, of the same 24″x36″ original would be 12″x18To learn more about 1 2 scale refers to:
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If the scale factor is a fraction, the shape will be smaller. This is the so-called recovery. So a scale factor of 1/2 means that the new shape is half the original shape.
What is Scale 1 2?Half scale is 1.
2. It is convenient to imagine that 1 unit on the drawing is equal to 2 units on the object. You can enlarge small objects and draw them on paper 2:
1 scale. This means that the drawing of the object is twice the size of the object itself.
This means that the units on the page represent "real life" units. If the drawing is drawn at half the actual size of the object, the scale is 1.
2. This means that 1 unit on the page is equivalent to 2 actual units.
These are references to the original drawing sizes. For example, if your drawing file is currently 24" x 36", it will be 24" x 36" when printed at full size. A print half the size of the same 24" x 36" original or a 50% reduction will be 12" x 18".
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Please help thankyou:)
Answers
The total volume of the object is 40 in³
What is the volume of a solid object?The volume of a solid object encompasses the space and capacity that the object can occupy. Here, we have two shapes that make up the solid object, a cylinder, and a sphere. A cylinder is an object that resembles a tube and has two circular sides with the same radius linked by a flat round surface.
The volume of the cylinder is calculated by using the formula:
V = πr²h
where; π = 3V = 3 * 2² * 3 ..... (since radius r = d/2 = 4/2 = 2)
V = 3 * 4 * 3
V = 36 in³
The volume of the sphere = 4/3 πr³
V = 4/3 * 3 * 1³
V = 4 in³
The total volume of the object = volume of the cylinder + volume of the sphere
The total volume of the object = 36 in³ + 4 in³
The total volume of the object = 40 in³
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find the area and peremiter of the parallelgram .
Answers
The area and perimeter of the parallelogram can be found to be :
Area Perimeter How to find the area and perimter of a Parallelogram ?The area of a Parallelogram can be found by the formula :
= Base of Parallelogram x Height of Parallelogram
= 54 in x 50 in
= 2, 700 in ²
The perimeter is simply the distance around the Parallelogram which is:
= 54 + 55 + 54 + 55
= 218 in
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#SPJ1Which of the following are statistics?
a. X
b. µ
c. α
d. s
e. α^2/n
Answers
Answer:
Letter B is the statistic.
What is a 3 2 scale factor?
Answers
Each of them becomes the fraction 3/2, or 1 1/2. (the second triangle is a little less than twice as big). Since we often keep the scale factor as a fraction, we would remark that it is 3/2.
How do you dilate by scale factor?We locate the dilation's centre point and measure the distances between it and other points on the preimage and the image in order to get the scale factor for the dilation. As correctly stated by Math Bits Notebook, the scale factor is determined by the ratio of these distances.The new shape is three times as large as the original if the scale factor is 3.The fundamental equation to determine the scale factor of a figure is written as, Dimensions of the original shape minus the dimensions of the new shape equals the scale factor.Scale Up = larger measurement / smaller measurement (smaller to larger).Smaller measurement / larger measurement equals a scale-down operation.To learn more about scale refer to:
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Each of them becomes the fraction 3/2, or 1 1/2. (the second triangle is a little less than twice as big). Since we often keep the scale factor as a fraction, we would remark that it is 3/2.
How do you dilate by scale factor?We locate the dilation's center point and measure the distances between it and other points on the preimage and the image in order to get the scale factor for the dilation. As correctly stated by Math Bits Notebook, the scale factor is determined by the ratio of these distances.
The new shape is three times as large as the original if the scale factor is 3.
The fundamental equation to determine the scale factor of a figure is written as, Dimensions of the original shape minus the dimensions of the new shape equals the scale factor.
Scale Up = larger measurement / smaller measurement (smaller to larger).
Smaller measurement / larger measurement equals a scale-down operation.
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What is substitution reaction explain with two examples?
Answers
The reaction in which one (or more) hydrogen atoms of a hydrocarbon are replaced by some other atoms (like chlorine), is called a substitution reaction.
Substitution reaction is a type of chemical reaction in which an atom, ion, or group of atoms or ions in a molecule is replaced by another atom, ion, or group.
The examples of substitution reactions are as follows:
1. Reaction of copper with zinc sulphate gives zinc with copper sulphate by replacing the zinc with copper.
[tex]Cu + ZnSO_{4}[/tex] → [tex]CuSO_{4} + Zn[/tex]
2. Reaction of magnesium with copper sulphate gives magnesium sulphate with copper by replacing copper with magnesium.
[tex]Mg + CuS0_{4}[/tex] → [tex]MgSO_{4} + Cu[/tex]
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How do you enlarge a shape by scale factor 3 center?
Answers
To employ a Centre of enlargement, lines must be drawn across the original shape's vertices at the center and through each of the edges. We refer to these as ray lines. E.g. The triangle ABC in this example has been scaled up by a factor of two around the enlargement's Centre, point O.
What is Centre of enlargement?By multiplying the original shape by a scale factor, we can change the size of the shape and make it bigger or smaller. This type of modification is called an expansion.To employ a Centre of enlargement, lines must be drawn across the original shape's vertices at the Centre and through each of the edges. We refer to these as ray lines.E.g.
In this instance, scale factor 1 has been used to increase triangle ABC.A Centre of enlargement point O is surrounded by 3 3 1s. The form gets smaller if the enlargement is between 0 0 and 1 1. The new triangle has the letters A, B, and C.The lengths of the new shape's sides are one-third that of the sides of the original shape.Parallel lines connect the groups of corresponding sides.The angles are the same in both shapes, and the triangles resemble one another.Mathematical mappings include transformations like enlargements. The word "maps" is thus frequently used in questions.An instruction in mathematics is a mapping, and an instruction in mathematics that affects a shape is a transformation.To Learn more About Centre of enlargement, refer To:
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To employ a Centre of enlargement, lines must be drawn across the original shape's vertices at the center and through each of the edges. We refer to these as ray lines. E.g. The triangle ABC in this example has been scaled up by a factor of two around the enlargement's Centre, point O.
What is Centre of enlargement?By multiplying the original shape by a scale factor, we can change the size of the shape and make it bigger or smaller. This type of modification is called an expansion.
To employ a Centre of enlargement, lines must be drawn across the original shape's vertices at the Centre and through each of the edges. We refer to these as ray lines.
E.g.
In this instance, scale factor 1 has been used to increase triangle ABC.
A Centre of enlargement point O is surrounded by 3 3 1s. The form gets smaller if the enlargement is between 0 0 and 1 1. The new triangle has the letters A, B, and C.
The lengths of the new shape's sides are one-third that of the sides of the original shape.
Parallel lines connect the groups of corresponding sides.
The angles are the same in both shapes, and the triangles resemble one another.
Mathematical mappings include transformations like enlargements. The word "maps" is thus frequently used in questions.
An instruction in mathematics is a mapping, and an instruction in mathematics that affects a shape is a transformation.
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What does it mean that stocks and bonds are relatively liquid? a. They are easier to buy and sell than other forms of investment. b. They tend to go up and down in value. c. The amount of income they can bring changes frequently. d. There are more of them to choose from than other forms of investment. Please select the best answer from the choices provided Group of answer choices A B C D
Answers
The correct option a. They are easier to buy and sell than other forms of investment, describes the relatively liquid.
Define the term relatively liquid bonds?A type of debt fund known as "liquid funds" mostly invests in higher financing instruments with 91-day maturities.
Liquid money are allocated to bank deposits, t - bills, bills of exchange, and other assets.Compared to other investment options, they are simpler to buy and sell. When an asset is described as liquid, it simply indicates that it can be quickly changed into cash. Because there will always be a buyer and a seller willing to exchange money for the stock or bond, liquid bonds and stocks are simpler to sell and buy.Thus,
Liquid assets are those that are challenging to buy, sell, or convert into cash.
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Help fast help I need help quick
Answers
On solving the provided question, we can say that the linear function that can be formed is x + 4y= 16 and rate of change in linear function is 13
What is linear function ?Two distinct but related concepts are referred to as linear functions in mathematics. A polynomial function of degree 0 or 1 is a linear function in calculus and related subjects if its graph is a straight line. Any function that depicts a straight line on a coordinate plane is said to be linear. For instance, y = 3x - 2 is a linear function since it depicts a straight line on the coordinate plane. f(x) = 3x - 2 can be used to represent the function since f(x) can be linked to y.
the linear function that can be formed is
x + 4y= 16
also, 2x = 26y
rate of change in linear function is 13
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Is section formula and midpoint formula same?
Answers
So on solving the provided question, we can say that A line segment's midpoint is the location where it is divided into two equally sized halves.
what is midpoint?The midpoint of a line segment is known as the midpoint in geometry. The centroid of all segments and ends, it is equally spaced from each of them. Add the two figures together and divide by two to determine the middle of any range. Look at this illustration to see how to determine the intersection of two points on a 1D axis. Consider the numbers 5 and 9 as the two points on a number line. Calculating the midpoint is as follows: (5 + 9)/2 = 14/2 = 7. As a result, 7 lies halfway between 5 and 9. There are instances when you need to locate a precise spot between two other points. The term "midpoint" refers to this center. The point on a line segment that divides the line is considered to be the midway of the segment.
A line segment's midpoint is the location where it is divided into two equally sized halves. The point splitting the line segment in any desired ratio can be found using the more potent section formula, which builds on the previous method.
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The scores earned in a flower-growing competition are represented in the stem-and-leaf plot.
0 5
1 0, 3, 7
2 4, 6, 8
3 2
4
5 8
Key: 5|8 means 58
What is the appropriate measure of variability for the data shown, and what is its value?
The range is the best measure of variability, and it equals 18.5.
The IQR is the best measure of variability, and it equals 45.
The range is the best measure of variability, and it equals 45.
The IQR is the best measure of variability, and it equals 18.5.
Answers
Answer:
(d) The IQR is the best measure of variability, and it equals 18.5.
Step-by-step explanation:
You want to know the best measure of variability for the data in the given stem-and-leaf plot.
0 | 51 | 0, 3, 72 | 4, 6, 83 | 24 |5 | 8StatisticsThe attachment shows the values of interest are ...
Range = 58 -5 = 53
IQR = 30 -11.5 = 18.5
Measure of variabilityYou can see from the shape of the stem-and-leaf plot that the mean and median are near 24, and most of the data is clustered in that neighborhood. The outlier at 58 skews the distribution to the right.
Since the data has an outlier, we choose the IQR as a better measure of the variability than the range is.
The IQR is the best measure of variability, and it equals 18.5.
__
Additional comment
Neither the IQR nor the range is 45. The range is definitely not 18.5. This means the answer choice we have selected is the only true statement about the data set. (It will often be the case that the only answer that is a true statement is the correct answer.)
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Which correctly describes how to determine the measure of angle 1? 2 parallel lines are crossed by a transversal to form 8 angles. clockwise from top left, the angles are 105 degrees, blank, blank, blank; blank, blank, 2, 1. the 105° angle and angle 2 are alternate exterior angles so angle 2 must measure 105°. angles 1 and 2 are supplementary angles so angle 1 must measure 75°. the 105° angle and angle 2 are corresponding angles so angle 2 must measure 105°. angles 1 and 2 are supplementary angles so angle 1 must measure 75°. the 105° angle and angle 2 are alternate exterior angles so angle 2 must measure 75°. angles 1 and 2 are supplementary angles so angle 1 must measure 105°. the 105° angle and angle 2 are corresponding angles so angle 2 must measure 75°. angles 1 and 2 are supplementary angles so angle 1 must measure 105°.
Answers
Option A is the correct answer. the 105° angle and angle 2 are alternate exterior angles so angle 2 must measure 105°. angles 1 and 2 are supplementary angles so angle 1 must measure 75°.
Two angles are called supplementary when their measures add up to 180° degrees. These angles form a straight angle when they are put together.
Angle 1 and angle 2 are supplementary if Angle1+Angle2= 180°.Thus, Angle 1 and Angle 2 are called "supplements" of each other.
Two angles that lie on opposite sides of the transversal and are placed on two different lines are called alternate exterior angles. These pairs of angles are always equal if the two given lines are parallel.
Two exterior angles that lie on two different lines cut by a transversal and are placed on opposite sides of the transversal are called alternate exterior angles.
Here,105 and ∠2 are alternate exterior angles, ∠2=105 degrees.
Angles 1 and 2 and supplementary
so 180 - ∠2 = ∠1
180-105=75.
∠1 =75 degrees.
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Answer:
A
Step-by-step explanation:
Lin ran 2 3/4 miles in 2/5 of an hour.
Noah ran 8 2/3 miles in 4/3 of an hour.
b. How long would it take Lin and Noah to run 1 mile at that rate? Show work on the sketch.
Answers
The time it would take Lin to run 1 mile is 8/55 hour
The time it would take Noah to run 1 mile is 2/13 hour
Calculating how long it would take to run 1 mileFrom the question, we are to calculate how long it would take Lin and Noah to run 1 mile
From the given information,
Lin ran 2 3/4 miles in 2/5 of an hour
Thus,
Lin's speed = (2 3/4) ÷ 2/5
Lin's speed = 11/4 ÷ 2/5
Lin's speed = 11/4 × 5/2
Lin's speed = 55/8 miles/hour
Now, to determine how long it would take Lin to run 1 mile
Using the formula,
Time = Distance / Speed
Time = 1 / (55/8)
Time = 8/55 hour
Also,
Noah ran 8 2/3 miles in 4/3 of an hour
Thus,
Noah's speed = (8 2/3) ÷ 4/3
Noah's speed = 26/3 ÷ 4/3
Noah's speed = 26/3 × 3/4
Noah's speed = 26/4
Noah's speed = 13/2 miles/hour
Now, to determine how long it would take Noah to run 1 mile
Using the formula,
Time = Distance / Speed
Time = 1 / (13/2)
Time = 2/13 hour
Hence, it will take 2/13 hour
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What is ed? enter your answer in the box. units two segments a d and b c intersect at point e to form two triangles a b e and d c e. side a b is parallel to side d c. a e is labeled 2 x plus 4. e d is labeled x plus 4. c d is 6. a b is 9.
Answers
The total area of the two triangles is 3 sq units + (-1 sq units) = 2 sq units.
The equation of line a b is y = 2x + 4
and the equation of line d c is y = x + 4
Substituting the y-coordinate of point E, (6) in the equations of line a b and d c, we get:
2x + 4 = 6
x + 4 = 6
Solving the above equations, we get x = 1 and y = 6.
Therefore, the coordinates of point E are (1,6).
The length of side a b is 9 - (2x + 4) = 9 - (2(1) + 4) = 3
The length of side d c is x + 4 - 6 = 1 + 4 - 6 = -1
The length of side a e is 2x + 4 - 6 = 2(1) + 4 - 6 = 2
The length of side d e is x + 4 - 6 = 1 + 4 - 6 = -1
Therefore, the area of triangle a b e is 1/2 (base x height) = 1/2 (3 x 2) = 3 sq units
The area of triangle d c e is 1/2 (base x height) = 1/2 (-1 x 2) = -1 sq units
Therefore, the total area of the two triangles is 3 sq units + (-1 sq units) = 2 sq units.
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Answer:
I am pretty sure it is 8 units.
Step-by-step explanation:
you need to rent a video camera for your school project. Murphy’s camera charges a $30 rental fee plus $35 per day. Allied rental charger is at $45 rental fee plus $30 per day. Which company should you choose?
Answers
Answer:
Step-by-step explanation:
Murphys camera
30+35 = $65 - Murphys is cheaper
45+30= $75
Taylor splits 5 pounds of ham equally to make 10 sandwiches. He thinks each sandwich will recieve 2 pounds of ham. Is he correct? explain
Answers
Answer: No
Step-by-step explanation: 5 pounds of ham would mean that 5 people get 1 pound, and 10 people would get 1/2 pound or 0.5 pounds of ham each.
Answer: No
Step-by-step explanation: Step 1: Calculate the total amount of ham needed for 10 sandwiches. This is 10 x 2 = 20 pounds.
Taylor is not correct, as he does not have enough ham to make 10 sandwiches with 2 pounds of ham in each.
Please help? This assignment is due in 23 minutes and is still have 7 more questions :(
The average person in a slum in a developing region uses 1.32 gallons (5 liters) of water every day. If the average shower in the US uses 7.5 gallons of water a minute how long of a shower would it be to use 1.32 gallons?
Answers
One gallon equals 16 eight ounce glasses of water.
A one-minute shower consumes how many gallons?According to the EPA, conventional shower heads utilize 2.5 gallons of water each minute. For the normal shower, that’s 20 gallons of water! To help lower your water impact, try trimming three minutes off your shower time. Delivering, purifying, and boiling hot water for your shower also consumes a lot of energy.
To determine the average shower water use, multiply the average flow rate of 2.1 gallons per minute by the average shower time of 8.2 minutes. So, 17.2 gallons is the average amount of water utilized. A 10-minute shower will consume 21 gallons of water. The amount of water consumed in the shower may quickly add up.
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Where can you buy a ruler that is 3 feet long worksheet answer key?
Answers
Therefore , the solution of the given problem of expression comes out to be 3 feet long ruler can be bought from yard sale.
What does expression actually mean?An analytical formula must be verified by replacing each parameter with a number or performing mathematical operations. Since 79 + 8 = 87, the response variable in the prior case is the same as 6. We can substitute values for the variables that we are familiar with in order to evaluate the expression.
Here,
Given : a ruler that is 3 feet long
where to buy
thus,
We can find the ruler which is 3 feet long can be bought from yard sale.
Therefore , the solution of the given problem of expression comes out to be 3 feet long ruler can be bought from yard sale.
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A line of best fit was drawn to the plotted points in a data set below. Based on the line of best fit, for what x-value does y=14y=14?
Answers
When Y=14 then x will be 20 for the given linear line (Linear equation).
What is a linear equation ?
A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form
Ax + B = 0
e.g. x-10=0. Here, x is a variable, A is a coefficient and B is constant.
The standard form of a linear equation in two variables is of the form
Ax + By = C
e.g. 2x-4y=10. Here, x and y are variables, A and B are coefficients and C is a constant.
Now,
As we can see from the graph that for values of y and x
y increase 3 points when x increase 5 points
e.g. (5,5) and (10,8)
Following the same trend when y=14 then x will be 20.
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When you write a number greater than or equal to 1 in scientific notation the exponent of the power of 10 will be?
Answers
When writing a number greater than or equal to 1 in scientific notation, the exponent of the power of 10 will be positive.
In scientific notation, a number is represented as a coefficient multiplied by a power of 10. For example, the number 12,000 can be written as 1.2 x 10⁴ in scientific notation.
When the number is greater than or equal to 1, the coefficient will be greater than or equal to 1 and less than 10. The exponent of the power of 10 will indicate the number of places the decimal point must be moved to the right to get the original number.
Since the number is greater than or equal to 1, the decimal point must be moved to the right, resulting in a positive exponent. So, when writing a number greater than or equal to 1 in scientific notation, the exponent of the power of 10 will always be positive.
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t = 3p/r + s
make r the subject of the formula
Answers
Answer:
\frac{3t}{t-1}[/tex]Step-by-step explanation:[tex]t = \frac{r}{r - 3}[/tex]Cross multiply,t(r - 3) = rtr - 3t = r tr = r + 3t tr - r = 3t r(t -1) = 3t
Step-by-step explanation:
Making the r as subject of the formula for the given expression t = 30p/r + s is given by, r = 30p/(t - s).
Given the expression is,
t = 30p/r + s, where p, r, s and t are mathematical variables.
We have to make the r the subject of the formula that is we have to express the variable ' r ' in terms of the other variables in the given expression.
t = 30p/r + s
t - s = 30p/r
r/30p = 1/(t - s)
r = 30p/(t - s)
Hence the rearranged form of the given expression is r = 30p/(t - s).
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If you pay $12.80 for 8 extra large bags of cheetos, how much will 1 bag cost you?
Answers
Answer:
12.80/8=1.6
$1.60 for one bag of cheetos
Step-by-step explanation:
Answer: $1.6 for 1 bag
Step-by-step explanation:
We can divide 12.80 by 8 = 1.6 to find the answer to your question
Expand & simplify 6 ( f + 5 ) − 4 ( f − 6 )
Answers
After simplification, the value of the expression is,
⇒ 2f + 54
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ 6 ( f + 5 ) - 4 ( f - 6 )
Now, Simplify the expression as;
⇒ 6 ( f + 5 ) - 4 ( f - 6 )
⇒ 6f + 30 - 4f + 24
⇒ 2f + 54
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Hideki buys 2 sweaters for $18 each. He can use one of the following coupons :
Coupon 1: Buy one, get one 40% off
Coupon 2: 25% off entire purchase
Which coupon should Hideki use to get a better deal?
Answers
Hideki should use coupon 2 to get a better deal.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Given that, Hideki buys 2 sweaters for $18 each.
Coupon 1: Buy one, get one 40% off
Here, 40% of 18
= 40/100 ×18
= 0.4×18
= $7.2
So, cost of entire purchase 2(18)-7.2
= 36-7.2
= $28.8
Coupon 2: 25% off entire purchase
25% of 2(18)
= 25/100 ×36
= 0.25×36
= $9
Now, 36-9 =$27
Therefore, Hideki should use coupon 2 to get a better deal.
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What is standard exponential form?
Answers
The Standard Exponential form is defined as the way of expressing a very large or very small number .
What is Standard Exponential form ?
The standard Exponential for is defined as a the representation of large numbers or small numbers. The exponents are used to represent such numbers in standard form.
The Steps to write a large number in exponential form are :
Consider the number 48600000000 ;
(i) Count the number of the trailing zeros in the given number.
(ii) Use the beginning of number to write digits from left till the last non-zero digit followed by a 10 raised to power equal to number of trailing zeros.
(iii) Place the decimal point after the first digit from the left side and add the number of decimal places created to the power of 10.
For example, in 48600000000 we place a decimal point after 4, then two decimal places will be created in the number 4.86 .
So, we will add 2 to the existing power of 10 , that was 8 as there were 8 trailing zeros, but now they become 10.
Therefore, the standard exponential form of the number 48600000000 is [tex]4.86 \times 10^{10}[/tex].
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can someone pls do this i'm lazy
Answers
Answer:
Here ya go lazy one
Step-by-step explanation:
1 - 0.62 x 2 = 1.24
2 - 0.5 x 9 = 4.5
3 - 3.6 x 8 = 28.8
4 - 5.1 x 7 = 35.7
5- 4 x 2.3 = 9.2
Mark me brainliest lazy one <3
How much will you pay for a hat that costs $24.99 if tax is 7.5%?
Answers
Answer:
The cost of the hat with 7.5% tax would be $26.87
Step-by-step explanation:
($24.99 * 0.075) = $26.87.
Find the values of a and b such that
X^2 + 2x - 7 = (x + a)^2 + b
Answers
The values of a and b are 1 and -8 respectively.
What are the values of a and b?[tex]x^{2} + 2x- 7 = (x+a)^{2}+b[/tex]
Let us consider the Right Hand Side of the given equation.
[tex](x+a)^{2}+b = x^{2} +2ax+a^{2} +b\\[/tex]
So,
[tex]x^{2} + 2x- 7 = x^{2}+2ax+a^{2}+b\\\\= x^{2}+2x(1)+1^{2}-8\\\\= (x+1)^{2} -8\\\\[/tex]
Here, a = 1 and b = -8
What is an equation?Equation is also known as a statement of equivalence between two expressions with variable and/or number-based components. Since equations are essentially questions, efforts to systematically find answers to those questions have been the driving force behind the development of mathematics. From straightforward algebraic equations that just require addition or multiplication to differential equations, exponential equations that use exponential expressions, and integral equations, there are many different types of equations that range in complexity. Numerous physics laws are expressed using them. likewise see equation system. The expressions on the left and right are shown to be equal to one another, demonstrating this relationship.To learn more about equation, refer:
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The table below shows Lamonte's earnings on the job.
Answers
Based on the constant rate of change, it will take Lamonte 4.5 hours to earn $107.55.
What is the constant rate of change?The constant rate of change refers to the ratio of an output value to an input which remains constant in all variables.
The constant rate of change is called a slope in a linear function or the unit rate.
The constant rate of change implies that the dependent variable changes (increasing or decreasing) as the other comparable or independent variable changes similarly.
Time (hours) Earnings (dollars) Unit Rate
3 $71.70 $23.90 ($71.70/3)
11 $262.90 $23.90 ($262.90/11)
28 $669.20 $23.90 ($669.20/28)
Total earnings = $107.55
Unit rate her hour = $23.90
The number of hours required = 4.5 hours ($107.55/$23.90)
Thus, using the constant rate of change or unit rate, Lamonte must work 4.5 hours to have total earnings of $107.55.
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A rectangle has a length of 5x+2 and a width of 3x-1. Write an Expression for the perimeter of the rectangle
Answers
Answer:
16x+6
Step-by-step explanation:
5x+2+3x+1+5x+2+3x+1 =
16x+6
Answer:
16x + 2
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{4 cm}\underline{Perimeter of a rectangle}\\\\$P=2(w+l)$\\\\where:\\ \phantom{ww}$\bullet$ $w$ is the width. \\\phantom{ww}$\bullet$ $l$ is the length.\\\end{minipage}}[/tex]
Given expressions:
[tex]\textsf{Length} = 5x + 2[/tex][tex]\textsf{Width} = 3x - 1[/tex]To write an expression for the perimeter of the rectangle, substitute the given expressions for the width and length into the perimeter formula:
[tex]\begin{aligned}\implies \textsf{Perimeter} &=2\left(5x+2+3x-1 \right)\\ &= 2(5x+3x+2-1)\\&=2(8x+1)\\&=16x+2\end{aligned}[/tex]